Geodesic
Orthogonality relations for deep level Deligne–Lusztig schemes of Coxeter type
Forum of Mathematics, Sigma, Tome 12 (2024)

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In this paper, we prove some orthogonality relations for representations arising from deep level Deligne–Lusztig schemes of Coxeter type. This generalizes previous results of Lusztig [Lus04], and of Chan and the second author [CI21b]. Applications include the study of smooth representations of p-adic groups in the cohomology of p-adic Deligne–Lusztig spaces and their relation to the local Langlands correspondences. Also, the geometry of deep level Deligne–Lusztig schemes gets accessible, in the spirit of Lusztig’s work [Lus76]. 
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     author = {Olivier Dudas and Alexander B. Ivanov},
     title = {Orthogonality relations for deep level {Deligne{\textendash}Lusztig} schemes of {Coxeter} type},
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Olivier Dudas; Alexander B. Ivanov. Orthogonality relations for deep level Deligne–Lusztig schemes of Coxeter type. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.55

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